The formulation of renormalization group running in QG is a
complicated problem because renormalizable and superrenormalizable
models of QG always have massive ghosts and other massive degrees
of freedom, such that the physical sense of
the the running (and quantum effects, in general) in these models is
not clear. The reason is that, loop contributions is these models
come from the functional integral over massless mode of the
gravitational field and, also, over the massive modes. It is a
standard assumption that the contributions of massive fields vanish
at the energy scale below their masses. In the fourth derivative QG
this expectation was formulated, for the first time, in [1]}.
Nowadays, it is partially supported by the calculations in
semiclassical theories [2]}, [3]} and in the toy model
of QG [4]}.
On the other hand, in QG all massive modes
have masses of the Planck order of magnitude (see the discussion
of this issue in [5]}). Thus, the physical applicability of
the renormalization group running in fourth- and higher-order
models of QG is restricted by the UV domain, with energies
above the Planck scale.
